Short Range Order Corrections to Alloy-Free Energies within the CALPHAD Framework Using the Cluster Variation Method Formalism.

The CALPHAD method, traditionally used to model experimental thermodynamic data, also provides an effective way to parametrize alloy free energies computed from first-principles. While the Special Quasirandom Structure (SQS) formalism offers a natural and efficient tool to generate input data for disordered solid solution phases, accounting for short range order (SRO) effects in a computationally efficient way presents a challenge. In this work we utilize the Cluster Variation Method (CVM) method in tandem with the SQS formalism to determine closed-form nonlinear expressions for temperature-dependent SRO corrections to the formation free energies. Our approach, which implements the CVM to any level of accuracy, has been integrated into the sqs2tdb software pipeline. As a proof of concept, we perform a thermodynamic assessment of the Ir-Ru binary alloy with SRO correction and show that under the tetrahedron approximation, the SRO correction to the hcp phase is sufficient to accurately reproduce the known experimental phase diagram.